Compactness of the Family of A(z)-Analytic Functions

In recent years, the Beltrami equation has garnered the attention of numerous researchers for the study of its analytical properties. Therefore, in this paper, we investigate certain properties of an analogue of the Cauchy integral for A(z)-analytic functions, utilizing the analytical properties of the Beltrami equation. Additionally, we obtain the compactness conditions for a family of functions within an A(z)-lemniscate.